{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T15:13:55Z","timestamp":1723216435600},"reference-count":34,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","funder":[{"name":"J C Bose National Fellowship provided by SERB, Government of India","award":["JBR\/2020\/000049"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2023,8]]},"abstract":" In this paper, we report the bifurcations of mode-locked periodic orbits occurring in maps of three or higher dimensions. The \u201ctorus\u201d is represented by a closed loop in discrete time, which contains stable and unstable cycles of the same periodicity, and the unstable manifolds of the saddle. We investigate two types of \u201cdoubling\u201d of such loops: (a)\u00a0two disjoint loops are created and the iterates toggle between them, and (b)\u00a0the length of the closed invariant curve is doubled. Our work supports the conjecture of Gardini and Sushko, which says that the type of bifurcation depends on the sign of the third eigenvalue. We also report the situation arising out of Neimark\u2013Sacker bifurcation of the stable and saddle cycles, which creates cyclic closed invariant curves. We show interesting types of saddle-node connection structures, which emerge for parameter values where the stable fixed point has bifurcated but the saddle has not, and vice versa. <\/jats:p>","DOI":"10.1142\/s0218127423300252","type":"journal-article","created":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T07:39:23Z","timestamp":1693813163000},"source":"Crossref","is-referenced-by-count":4,"title":["Bifurcations of Mode-Locked Periodic Orbits in Three-Dimensional Maps"],"prefix":"10.1142","volume":"33","author":[{"given":"Sishu Shankar","family":"Muni","sequence":"first","affiliation":[{"name":"Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Campus Road, Mohanpur, West Bengal 741246, India"}]},{"given":"Soumitro","family":"Banerjee","sequence":"additional","affiliation":[{"name":"Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Campus Road, Mohanpur, West Bengal 741246, India"}]}],"member":"219","published-online":{"date-parts":[[2023,9,4]]},"reference":[{"key":"S0218127423300252BIB001","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1134\/1.2121837","volume":"31","author":"Anishchenko V.","year":"2005","journal-title":"Tech. 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